Abstract
Investigation of the free vibration of structural elements or structures often requires the calculation of certain natural frequencies and modes using equations from the three-dimensional theory on elasticity. Other studies have focused on the numerical investigations of problems in such a formulation. Here we propose a new approach to determining the frequencies and modes of piecewise-uniform axisymmetric bodies by means of the three-dimensional theory of elasticity. Cauchy relations are set up eith a matrix of differential operators and the Bubnov-Galerkin method is used to determine the eigenfrequencies and modes of free vibration.
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